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Theorems · Theorem · order theory

Order.Iic_succ

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : SuccOrder α] (a : α),
  Set.Iic (Order.succ a) = insert (Order.succ a) (Set.Iic a)
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
2 results in Mathlib
Foundations
Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderSuccOrder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Order.Icc_succ_right · cited by 0Order.Icc_succ_rightOrder.Ioc_succ_right · cited by 0Order.Ioc_succ_rightSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.ext · cited by 2266Set.extSet.Iic · cited by 1111Set.IicOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderOrder.le_succ_iff_eq_or_le · cited by 6Order.le_succ_iff_eq_or_leOrder.Iic_succCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.